Parabolic antenna system having high-illumination and spillover efficiencies

ABSTRACT

An antenna feed system which simultaneously produces nearly uniform amplitude and phase illumination as well as high spillover efficiency, in a parabolic antenna, is composed of a feed or horn source and an interposed dielectric element. The dielectric element diffracts the emitted energy to maximize the spillover and illumination efficiencies. These efficiencies are increased by configuring the surface of the interposed dielectric element. In one species the interposed element is a lens and in another is a reflector coated with dielectric material.

United States Patent [191 Bartlett et al.

[4 1 June 5,1973

[54] PARABOLIC ANTENNA SYSTEM HAVING HIGH-ILLUMINATION AND SPILLOVEREFFICIENCIES [75] Inventors: Homer E. Bartlett, Melbourne, Fla.; EmoryL. Sheppard, Morrisville, NC.

[73] Assignee: Radiation Incorporated, Melbourne,

Fla.

[22] Filed: June 18, 1970 [21] Appl. No.: 47,378

2,705,753 4/1955 .Iaffe ..343/755 3,162,858 12/1964 Cutler .343/8403,264,648 8/1966 Sundberg et al. ..334/754 3,392,395 7/1968 I-Iannan..343/755 3,430,244 2/1969 Bartlett et al ..343/755 FOREIGN PATENTS ORAPPLICATIONS 973,583 10/1964 Great Britain; ..343/84O 1,163,156 9/1969Great Britain ..343/755 Primary Examiner-Eli Lieberman Attorney-Yountand Tar'olli [57] ABSTRACT An antenna feed system 7 which simultaneouslyproduces nearly uniform amplitude and phase illumination as well as highspillover efficiency, in a parabolic antenna, is composed of a feed orhorn source and an interposed dielectric element. The dielectric elementdiffracts the emitted energy to maximize the spillover and illuminationefficiencies. These efficiencies are increased by configuring thesurface of the interposed dielectric element. In one species theinterposed element is a lens and in another is a reflector coated withdielectric material.

9 Claims, 5 Drawing Figures PAFENTEB 3,737, 909

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ATTORNEYS OUNDRRY B i uuamnuu BOUNDARY BOUNDARY BOUNDARY PARABOLICANTENNA SYSTEM HAVING HIGH-ILLUMINATION AND SPILLOVER EFFICIENCIESBACKGROUND OF THE INVENTION Various types of antenna systems are knownin the prior art. One of these systems utilizes a reflecting elementwhich is parabolically configured and which has a source of energy atits focal point. The energy emitted by the energy source istheoretically reflected from theparabolic reflector in substantiallyparallel rays. Although the following description is directed to atransmitting antenna system, the description is equally applicable to areceiving antenna.

Various attempts have been made to maximize the efficiency of suchantenna systems. One such system is the Cassegrain. In this type ofantenna system, a parabolic main reflector is used and a hyperbolicsubreflector is located near the focal point of the parabolic mainreflector. An energy source is then located near the hyperbolicsubreflector. The energy emitted by the energy source is reflected bythe subreflector onto the parabolic main reflector and out into theatmosphere.

' The over-all efficiency of such an antenna system is determinedprimarily by the ability of the energy source to illuminate thereflector uniformly across its surface. This is commonly referred to asthe illumination efficiency. Another determining factor of the over-allefficiency of such an antenna system is the spillover efficiency. Thisis the ability of the subreflector m uniformly illuminate the mainreflector while minimizing the energy which passes the edges of the mainreflector.

To some extent these two efficiencies are inconsistent. This is sobecause the maximization of the illumination efficiency requires theedges of the main reflector to be illuminated to the same extent thatits interior portions are illuminated. This inherently results in anincrease of the radiation spillover and thereby decreases the spilloverefficiency. Likewise, an attempt to decrease the energy spillover andthereby increase the spillover efficiency results in a decrease of theillumination along the edges of the reflector and a decrease in theillumination efficiency results. This difficulty has been recognized inthe past and has been partially solved by compromising between the twoefficiencies. Accordingly, most prior art antenna systems compromisebetween the illumination and the spillover efficiencies so that each arein the order of 75 to 80 per cent. These efficiencies are about thehighest obtainable by conventional technology.

One known system has greatly improved these theoretical and practicalefficiencies in a Cassegrain system such that a theoretical 100 percentillumination efficiency is obtainable while increasing the spilloverefficiency to above 90 per cent. This system is basedon the principlethat planned deviations of the hyperbolic subreflector and parabolicmain reflector from the hyperbolic and parabolic configurations canresult in the above noted increases in efficiencies.

An article entitle High Efficiency Antenna Reflector" by William F.Willaims, published in the July 1965 issue of The Microwave Journal onpages 79 to 82 describes an antenna system which improved theillumination and spillover efficiencies of a Cassegrain antenna system.The article presents a mathematical analysis showing that deviations ofthe sort mentioned above results in increases of the illumination andspillover efficiencies. Although the antenna system described in thearticle is a theoretical improvement of the other prior art antennasystems it has several practical disadvantages. As a practical matter,it is more expensive to manufacture a reflector which conforms to therequired configuration. Also, the technique described does not allow forthe optimization of antenna systems which are already in use.

SUMMARY OF THE INVENTION The inventive antenna system contains adielectric refractive element to refract the energy emitted from theenergy source so that the main reflector is uniformly illuminated overits entire surface while the energy spillover around its edge isminimized. These two results are achieved by forming the surface of therefracting element according to equations derived for an antenna systemhaving a parabolic main reflector. The inventive system therefore ismore practical than the system describe in the Microwave Journal articlefully referenced hereinabove. Because a parabolic main reflector isused, existing manufacturing procedures can be used. For this reason theinventive antenna system is more economical and mechanically feasiblethan the prior art systems.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a first preferred embodimentof the inventive system utilizing a reflective subreflector.

FIG. 2 is a second preferred embodiment of the inventive systemutilizing a shaped lens which is transparent to the energy emitted bythe energy source.

FIGS. 3, 4 and 5 are diagrams useful in developing the equations whichdefine the configurations of the refracting elements. Y

DESCRIPTION OF THE PREFERRED EMBODIMENTS bolic reflector 10. Solid lines16, 17, 18, and 19 are i used to illustrate the path of radiation fromthe energy source 15 through the dielectric coat 14 and to the reflector10 out to the atmosphere from the reflector. Broken line 20 is used asan extension of line 18 to show that the radiation appears to emanatefrom the focus point 12 located at a point P Only half of the parabolicreflector 10 is shown in the figure; actually,

- the reflector 10 is symmetrical about the X axis and also has radialsymmetry about this axis. Reflector 11 also is radially symmetricalabout the X axis. Reflector 11 has two irregularsurfaces.Reflective-element 13 is bonded, or otherwise fixed to one of thesesurfaces. The other surface is indicated by reference number 21. Both ofthese surfaces are irregular, and they can have differentconfigurations. The exact configurations are defined by a set-ofequations whichare based on the parameters of the antenna system, andthe dielectric constant of coating 14. The illumination efficiency isoptimized and the spillover efficiency I is greatly increased byconfiguring the two surfaces of the refractor 11 in accordance withthese equations and their development is presented hereinafter.

FIG. 2 is a second preferred embodiment of the invention. Thisembodiment also employs a parabolic reflector 10. A shaped lens 26,which is transparent to the radiation emitted by the energy source 27,is located in the vicinity of the focal point 23 of the parabolicreflector 10. Lens 26 is composed of a dielectric material such asquartz or polypropylene. The two irregular surfaces 29 and 30 of lens 26are configured such that the energy passing through the lens optimizesthe illumination efficiency of the reflector 10. The configurationsrequired for this optimization are also defined by a set of equationsbased on the same types of considerations as those of the FIG. 1embodiment.

The FIG. 2 solid lines 31, 32, 33 and 34 are used to show the path ofthe radiation from the feed source 27 through the lens 26, its pathbetween refractor 26 and reflector 10, and its reflection from thereflector 10. In both FIGS. 1 and 2 the line A-B is used to represent asurface upon which constant amplitude and phase illumination is desired.

The primary difference between the FIG. 1 and FIG. 2 embodiments lies inits refractive elements 11 and 26. In FIG. 1 a reflective surface 13reflects the energy back through the dielectric 14. Consequently energysource 15 is positioned between refractor l1 and reflector 10. In FIG. 2refractor 26 has no reflective surface. Energy therefore passes throughthe dielectric lens 26 only once. Lens 26 is therefore positionedbetween energy source 27 and reflector 10.

The refractive elements 11 and 26 are very similar, in that they bendthe energy after it emanates from the energy source but before itreaches parabolic reflector 10. They are also similar because they bothhave two irregular surfaces defined by equations developed by using thesame system criterion. Lens 26 and refractor 11 are symmetrical aboutthe X axis and their axis of symmetry are coincident with the axis ofsymmetry or reflector 10. The mean thickness of lens 26 and refrac-. tor11 can be as thin as a fraction of an inch and can exceed inches.v

Both refractive elements 11 and 26 respectively shown in FIGS. 1 and 2are designed such that the percentage of the energy from the energysource which is contained within the solid angle 0 is equal to thepercentage of the aperture area contained within a circle of radius X.The aperture illumination is therefore very nearly uniform. Also, thedesign configurations of the refractive elements 1 1 and 26 are suchthat the energy leaving the dielectric refractor (11 or 26) must have aspherical phase front about point P Theresult ofshaping the surfaces oflens 26 and refractor 11 as dictated by the equations set forthhereinafter invariably will result in the surfaces being irregular inconfiguration. However, the configurations shown in the figures are notnecessarily those which will be derived for every instance. The shapesof the surfaces will be dependent upon the design parameters of theantenna system as well as the dielectric constant of the material usedto construct the refractive element 11 or 26.

Q (1cos B )F(0) sin 0 sin B JL FW) Sin 0110 (3) tan a (a sin [3 rsin0)/(P P a cos/3 r 0050) where: e is the dielectric constant of thedielectric lens 26, all other variables are defined by FIG. 2.

In equation (3) the maximum value of B is 6by [3 and represents theangle from the edge of the parabolic reflector 10. Likewise, l9,, is themaximum value of 18 at which an electromagnetic ray from P, will berefracted by the lens 26 at an angle 5,, to the edge of the parabolicreflector 10. I

Equation (1) is written with Snells Law of Refraction at surface 29. Itis used to relate the slope of surface 29 to the angles 0 and a. I

Equation (2) is written with Snells Law of Refraction 'at surface 30. Itis used to relate the angles B and l a to the slope of surface 30. Italso requires the energy leaving the lens 26 to have a constant phaseabout point P P is the focal point 'of parabolic reflector 10.

P, is the origin of the polar coordinate system r,0 and also the phasecenter of the feed source 27..

In equation (4) P, P is the distance between points P and P2.

A better understanding of equations (1) (4) can be obtained by viewingtheir development.

Equation (1) is developed by use of Snells Law of Refraction at surface29. For convenience and clarity those portions of FIG. 2 required forthe development of equation (I) are shown in FIG. 3. Y

From FIG. 3:

6, 8 because of the dielectric constant e of the lens material \/?sin 8sin 8, l

I i I (lb) (dr/rdO) tan 7 tan a,

I (i VZsin (0 8, a) sin 8,

and

' -(dr/rd) =sin (6a)/(l\/ e) cos 0-41 h in Equation (2) is developedwith Snells Law of Refraction at surface 30 Here, for purposes ofconvenience and clarity those portions of FIG. 2 required for thedevelopment of equations (2) are repeated in FIG.

mm FIG. 4;

da/adB tan 7 tan (W B -01) V's sin I, sin 1',

vsin I, sin (B-a-i-I'o I sin (B-a) cosl', cos (B-a) sin I,

VZ= cotl' sin (3-01) cos (B-a) I I (2d) 'r v? 99 (B-Mi/ (8- V I I z)tanl', sin (B-OOII cos (3-01)] f a sinB r sin0 g P,P2 a cost? --r c080 wtana (a sinB r sin0)/(P,P,+ a cosfl r c050) FIG.- 2 and equations l (4)related thereto are directed to an antenna utilizing a transparent lens26 to optimize the illumination efficiency. FIG. 1 shows an antennasystem which utilizes a dielectric coated subreflector-as the energyrefracting device. The geometry of the two antenna systems thereforevaries slightly However, the same principles apply.

and

da/adB vat-n (B-a)! vicosm-a -l Equation (3) is derived from theconservation of en-' ergy principle as follows:

, L 1m sin 0d(i=J:I(B) sin ads Integration of the right side ofequations (30) and (3b) while holding l (fl) constant, subsequentdivision of (3a) by (3b) and their differentiation of the result withrespect to 0 yields:

sin 5J1 F(6) sm 0110 (3) FIG. 5 combines the portions of FIGS. 3 and 4necessary to an understanding of equation (4).

From HO. 5:

tana= f/g Equations (5) through (10) are-presented below as thosedefining the boundary surfaces 13 and 21 of the FIG. 1 embodimentnecessary to optimize the illumination efficiency of an antennautilizing a dielectric coated subreflector.

Equations (5) and (6) are developed by use of Snell's Law of Refractionat surface 21 in a manner very similar togEquations (1) and (2'). Thesymbol e is the "dielectric constant of coating l4.

Equation (5) relates the slope of surface 21 to the'an- I I gles 6 and0:. Equation (6) relates the slope of surface 13 to the angles B and g.

Equation (7) is the same as Equation (3). Some manipulation of thisequation shows that the energy density as a function of B is see 5/2 for0 p p, and

zero for B [3,. Uniform amplitude distribution "at I Plane AB resultsfrom this relationship.

Equation (8) is developedjby use of- Snell's Law-of" Refraction atsurface 13 and relates the slope of surface 13 to the angles a and g. d

Equations (9) and (10) relate the points of surface 13 to those ofsurface 21. in equations (9) and (10) ,t

and y respectively refer "to the horizontal and vertical coordinates ofa coordinate system having its origin at 2.

Because the same basic principles' apply to equations I (l)-'(4) andequations (5) through 10) the full development of the last set ofequations isnot presented. I

The problem of optimizing the illumination efficiency of a parabolicantenna system while simultaneously increasing the spillover efficiencyhas been solved by the invention. The solution lies in providing theantenna system with an energy refraction device interposed between theenergy source and the main parabolic reflector. The two surfaces of therefracting device are irregularly formed according to a set of equationsbased upon the parameters of the antenna system. The equations aredeveloped for an antenna system having a parabolic reflector andtherefore the invention is very practical from both a theoretical and amanufacturing view point. The use of a parabolic main reflector alsomakes antenna systems in accordance with the invention and therebygreatly improve their illumination and spillover efficiencies.

While we have described and illustrated specific embodiments of ourinvention, it will be clear that variations of the details ofconstruction which are specifically illustrated and described may beresorted to without departing from the true spirit and scope of theinvention as defined in the appended claims.

We claim:

1. An antenna system having a main focusing means for redirecting energyhaving a focus proximate the axis of symmetry of said main focusingmeans and a feed device having a phase center proximate the axis ofsymmetry, said antenna system including a dielectric energy refractingmeans through which a beam transmitted between said main focusing meansand said feed device passes, said refracting means having a firstirregular surface means at which energy is redirected and substantiallywholly comprising segments whose slopes are each a function of beamintensity at the segment to redirect the beam across an interveningspace to a boundary at which the intensity of the beam has a relativedistribution within the beam different fromthat of the beam at the firstsurface means, and a second irregular surface means at said boundarycomprising a plurality of segments having slopes which are a function ofthe directions of the redirected beam at the segments for furtherredirecting the beam to proceed along a course comprising linesextending from one of said focus and center, said slopes of the segmentsof one of said irregular surface means of said refracting means being afunction of a first angle between the axis of symmetry of said mainfocusing means and the apparent line of travel of energy through saidfocus and a second angle formedbetween the axis of symmetry and the lineof travelof said energy through said refracting means, and said slopesof the segments of the other of said irregular, surface means being afunction of said second angle and of a third angle between the axis ofsymmetry and the apparent line of travel of energy through said phasecenter.

2. The antenna system of claim 1 wherein said energy refracting means isatransparent lens; and the two surface means of the lens are defined bythe equations:

da/adp sin 5 a)/ x/ costfi a) -1 .flLQi @2160) a e tan a (a sin ,8 r sin0)/(P P a cos B r cos 0) wherein:

a the distance from said focus to said one surface means 7 i e thedielectric constant of said refracting means [3 said first angle [3,,maximum value of B a said second angle r the distance from said phasecenter to said other of said surface means 0 said third angle 0, maximumvalue of 0.

3. The antenna system of claim 1 wherein said refracting means islocated between said feed device and said main focusing means; andwherein substantially all of the energy coupled to said feed devicepasses through said refracting means.

4. An antenna system as defined in claim 1 and wherein a relativedistribution of intensity of the reflected beam resulting external tothe antenna is substantially uniform, and wherein said beam has a firstphase front about said focus and has a second phase front about saidphase center and at least one of said first and second phase fronts isapproximately spheri cal. I

5. An antenna system having a main focusing means for redirecting energyhaving a focus proximate the axis of symmetry of said main focusingmeans and a feed device having a phase center proximate the axis ofsymmetry, said antenna system including a dielectric energy refractingmeans through which a beam transmitted between said main focusing meansand said feed device passes, said refracting means having a firstirregular surface means at which energy is redirected and substantiallywholly comprising segments whose slopes are each a function of beamintensity at the segment to redirect the beam across an interveningspace to a boundary at which the intensity of the beam has a relativedistribution within the beam different from the beam redirected by thefirst surface means, and a second irregular surface means at saidboundary comprising a plurality of segments having slopes which are afunction of the directions of the redirected beam at the segments forfurther redirecting the beam to proceed along a source comprising linesextending from one of said focus and center, said refracting meansincluding highly reflective means on one of said irregular surfacemeans, said refracting means being arranged so that energy in said beampasses in a first direction through the other of said surface means andthrough said refracting means and impinges upon said reflective meansand passes through aid refracting means in a second direction betweensaid reflective means and through said other surface means, said slopesof said other of said surface means being a function of a first angleformed between said axis of symmetry of the main focusing means and theline of travel of said energy along lines extending from the focal pointof said main focusing means and a second angle formed between said axisand the line of travel of said energy as it passes through saidrefraction means, said slopes of the one of said surface means havingsaid reflective means being a function of said second angle and a thirdangle formed between said axis and the line of travel of said energy asit passes in said second direction through said refracting means; andsaid slopes of the other of said surface means of said refracting meansbeing a function of said third angle and a fourth angle formed betweenthe axis of symmetry of said main focusing means and the line of travelof said energy along lines extending from said phase center.

6. the antenna system of claim 5 wherein said reflective means on saidone surface means and said other surface means are defined by theequations:

dr/rdfl J? sin (a)/ t/Z cos (0-0:) 1

da/adB t/Z sin (p)/ 1/? cos a-g 1 (1cos B F(0) sin 0 a0 sin Bf? F(0) sin0010 dx/dy tan a)/2 a tan (y r sin 0)/P P x r cos 0) (f tan (a sin By)/(a cos B x) wherein:

e the dielectric constant of said refracting means a the distance fromsaid focus to said other of said surfaces along said lines extendingfrom said focal point B said first angle B maximum value of B 5 saidsecond angle 0 said fourth angle 0 maximum value of 0 a said third angler the distance from said phase center to said other surface along saidlines extending from said phase center .1: a coordinate of a rectangularcoordinate system having its origin at said first focal point, extendingalong said axis y a coordinate of said coordinate system extendingtransversely to said axis.

7. The antenna system of claim 1 wherein said highly reflective means isa metallic surface; and wherein said feed device is located between saidrefracting means and said main focusing means; said refracting meansbeing situated between said metallic surface and said feed device.

8. An antenna system as defined in claim 5 and wherein a relativedistribution of intensity of the reflected beam resulting external tothe antenna is substantially uniform, and wherein said beam has a firstphase front about said focus and has a second phase front about saidphase center and at least one of said first and second phase fronts isapproximately spherical.

9. An antenna apparatus for transmitting or receiving electromagneticpower comprising main focusing means for redirecting power with aprincipal axis and having a geometric focus, and a feed device having aphase center and a power density pattern F(0), comprising lens meanshaving first and second boundary portions for changing the direction ofpropagation of electromagnetic power received thereon, the power betweensaid phase center and said main focusing means being a beam having afirst segment at least a portion of which is between said phase centerand lens means and a second segment at least a portion of which isbetween said lens means and said main focusing means, said first andsecond boundaries extending generally transversely of the axis and saidsecond boundary being offset a distance along the beam route-from thefirst means in a downstream direction for power flow, said first beamsegment being directed along lines emanating from said phase center atvarious directional angles 0 up to an angle 6, said second beam segmentbeing directed along lines emanating from said focus at variousdirectional angles B up to an angle B both 0 and B being measured fromthe principal axis, said apparatus having a first phase wavefront shapeand a first power density distribution H0) in the first beam segment upto the angle 0, and having a substantially spherical second phasewavefront shape and a substantially uniform second power densitydistribution of said beam as measured with respect to the angle B in thesecond beam segment up to the angle B,,,, said first means receiving oneof said beam segments and being configured to be comprised ofdifferential segments for redirecting by differing amounts the portionsof received beam power received upon the segments at differing distancesfrom said axis and cooperating with said offset distance to convert thepower density distribution within said beam to the'distribution in theother of said beam segments, said second boundary being configured to becomprised of a plurality of differential segments for redirecting bydiffering amounts the portions of beam power received upon segments atdiffering distances from said axis to follow lines emanating at angles 0and B respectively from one of said center and focus, and wherein theportions of beam power flowing at any directional angle 0 in the firstsegment flow at a respective directional angle Bin accordance with therelationship

1. An antenna system having a main focusing means for redirecting energyhaving a focus proximate the axis of symmetry of said main focusingmeans and a feed device having a phase center proximate the axis ofsymmetry, said antenna system including a dielectric energy refractingmeans through which a beam transmitted between said main focusing meansand said feed device passes, said refracting means having a firstirregular surface means at which energy is redirected and substantiallywholly comprising segments whose slopes are each a function of beamintensity at the segment to redirect the beam across an interveningspace to a boundary at which the intensity of the beam has a relativedistribution within the beam different from that of the beam at thefirst surface means, and a second irregular surface means at saidboundary comprising a plurality of segments having slopes which are afunction of the directions of the redirected beam at the segments forfurther redirecting the beam to proceed along a course comprising linesextending from one of said focus and center, said slopes of the segmentsof one of said irregular surface means of said refracting means being afunction of a first angle between the axis of symmetry of said mainfocusing means and the apparent line of travel of energy through saidfocus and a second angle formed between the axis of symmetry and theline of travel of said energy through said refracting means, and saidslopes of the segments of the other of said irregular surface meansbeing a function of said second angle and of a third angle between theaxis of symmetry and the apparent line of travel of energy through saidphase center.
 2. The antenna system of claim 1 wherein said energyrefracting means is a transparent lens; and the two surface means of thelens are defined by the equations: - (dr/rd theta ) sin ( theta - Alpha)/(1/ Square Root epsilon ) - cos ( theta - Alpha ) (1) da/ad BetaSquare Root epsilon sin ( Beta - Alpha )/ Square Root epsilon cos (Beta - Alpha ) - 1 (2) tan Alpha (a sin Beta - r sin theta )/(P1 P2 + acos Beta - r cos theta ) (4) wherein: a the distance from said focus tosaid one surface means epsilon the dielectric constant of saidrefracting means Beta said first angle Beta m maximum value of BetaAlpha said second angle r the distance from said phase center to saidother of said surface means theta said third angle theta m maximum valueof theta .
 3. The antenna system of claim 1 wherein said refractingmeans is located between said feed device and said main focusing means;and wherein substantially all of the energy coupled to said feed devicepasses through said refracting means.
 4. An antenna system as defined inclaim 1 and wherein a relative distribution of intensity of thereflected beam resulting external to the antenna is substantiallyuniform, and wherein said beam has a first phase front about said focusand has a second phase front about said phase center and at least one ofsaid first and second phase fronts is approximately spherical.
 5. Anantenna system having a main focusing means for redirecting energyhaving a focus proximate the axis of symmetry of said main focusingmeans and a feed device having a phase center proximate the axis ofsymmetry, said antenna system including a dielectric energy refractingmeans through which a beam transmitted between said main focUsing meansand said feed device passes, said refracting means having a firstirregular surface means at which energy is redirected and substantiallywholly comprising segments whose slopes are each a function of beamintensity at the segment to redirect the beam across an interveningspace to a boundary at which the intensity of the beam has a relativedistribution within the beam different from the beam redirected by thefirst surface means, and a second irregular surface means at saidboundary comprising a plurality of segments having slopes which are afunction of the directions of the redirected beam at the segments forfurther redirecting the beam to proceed along a source comprising linesextending from one of said focus and center, said refracting meansincluding highly reflective means on one of said irregular surfacemeans, said refracting means being arranged so that energy in said beampasses in a first direction through the other of said surface means andthrough said refracting means and impinges upon said reflective meansand passes through aid refracting means in a second direction betweensaid reflective means and through said other surface means, said slopesof said other of said surface means being a function of a first angleformed between said axis of symmetry of the main focusing means and theline of travel of said energy along lines extending from the focal pointof said main focusing means and a second angle formed between said axisand the line of travel of said energy as it passes through saidrefraction means, said slopes of the one of said surface means havingsaid reflective means being a function of said second angle and a thirdangle formed between said axis and the line of travel of said energy asit passes in said second direction through said refracting means; andsaid slopes of the other of said surface means of said refracting meansbeing a function of said third angle and a fourth angle formed betweenthe axis of symmetry of said main focusing means and the line of travelof said energy along lines extending from said phase center.
 6. theantenna system of claim 5 wherein said reflective means on said onesurface means and said other surface means are defined by the equations:dr/rd theta Square Root epsilon sin ( theta - Alpha )/ Square Rootepsilon cos ( theta - Alpha ) - 1 (5) da/ad Beta Square Root epsilon sin( Beta - xi )/ Square Root epsilon cos ( Beta - xi ) - 1 (6) dx/dy - tan( xi - Alpha )/2 (8) Alpha tan 1 (y - r sin theta )/P1P2 - x - r costheta ) (9) xi tan 1 (a sin Beta - y)/(a cos Beta - x) (10) wherein:epsilon the dielectric constant of said refracting means a the distancefrom said focus to said other of said surfaces along said linesextending from said focal point Beta said first angle Beta m maximumvalue of Beta xi said second angle theta said fourth angle theta mmaximum value of theta Alpha said third angle r the distance from saidphase center to said other surface along said lines extending from saidphase center x a coordinate of a rectangular coordinate system havingits origin at said first focal point, extending along said axis y acoordinate of said coordinate system extending transversely to saidaxis.
 7. The antenna system of claim 1 wherein said highly reflectivemeans is a metallic surface; and wherein said feed device is locatedbetween said refracting means and said main focusing means; saidrefracting means being situated between said metallic surface and saidfeed device.
 8. An antenna system as defined in claim 5 and wherein arelative distribution of intensity of the reflecTed beam resultingexternal to the antenna is substantially uniform, and wherein said beamhas a first phase front about said focus and has a second phase frontabout said phase center and at least one of said first and second phasefronts is approximately spherical.
 9. An antenna apparatus fortransmitting or receiving electromagnetic power comprising main focusingmeans for redirecting power with a principal axis and having a geometricfocus, and a feed device having a phase center and a power densitypattern F( theta ), comprising lens means having first and secondboundary portions for changing the direction of propagation ofelectromagnetic power received thereon, the power between said phasecenter and said main focusing means being a beam having a first segmentat least a portion of which is between said phase center and lens meansand a second segment at least a portion of which is between said lensmeans and said main focusing means, said first and second boundariesextending generally transversely of the axis and said second boundarybeing offset a distance along the beam route from the first means in adownstream direction for power flow, said first beam segment beingdirected along lines emanating from said phase center at variousdirectional angles theta up to an angle theta m, said second beamsegment being directed along lines emanating from said focus at variousdirectional angles Beta up to an angle Beta m, both theta and Beta beingmeasured from the principal axis, said apparatus having a first phasewavefront shape and a first power density distribution F( theta ) in thefirst beam segment up to the angle theta m, and having a substantiallyspherical second phase wavefront shape and a substantially uniformsecond power density distribution of said beam as measured with respectto the angle Beta in the second beam segment up to the angle Beta m,said first means receiving one of said beam segments and beingconfigured to be comprised of differential segments for redirecting bydiffering amounts the portions of received beam power received upon thesegments at differing distances from said axis and cooperating with saidoffset distance to convert the power density distribution within saidbeam to the distribution in the other of said beam segments, said secondboundary being configured to be comprised of a plurality of differentialsegments for redirecting by differing amounts the portions of beam powerreceived upon segments at differing distances from said axis to followlines emanating at angles theta and Beta respectively from one of saidcenter and focus, and wherein the portions of beam power flowing at anydirectional angle theta in the first segment flow at a respectivedirectional angle Beta in accordance with the relationship